"That's the big deer from Edward Scissorhands," a woman in the sculpture garden of New York's Museum of Modern Art tells her friend, pointing at an outsized topiary stag based on the one in Tim Burton's 1990 film. "And I recognise this one from Beetlejuice, when the furniture tries to eat [the characters]," she adds, gesturing at a large, pointy, painted sheet-metal piece that bears a passing resemblance to something from Burton's 1988 movie but is in fact Alexander Calder's 1959 sculpture Black Widow.

The attribution might have been wide of the mark but at least a connection was made between Burton and a larger artworld. The peculiar thing about Moma's Tim Burton show, which has been running since November and continues to the end of April, is how little effort its curators have made to glance backward or sideways to place Burton's work within a broader context.

Burton has a distinctive sensibility, consistently expressed with wit, imagination and macabre charm, but he is not an obvious candidate for a blockbuster show at one of the world's most prestigious art museums. Part of the exhibition's job is surely to offer an argument about why he should be given a platform alongside the likes of Claude Monet and William Kentridge, both of whom also have shows at Moma at the moment, and how his work fits into and enhances a larger cultural narrative. This the exhibition does not do.

Instead, it gives us Burton, Burton and more Burton. You can see why: the man is plainly prodigious and each of the hundreds of pieces on show has its own reasons to be admired – from early Mad magazine-influenced cartoons and public-service posters created by Burton as a teenager in Burbank, California, to props and production work from his movies (Edward Scissorhands's leather-switchblade costume, The Nightmare Before Christmas's Jack Skellington figure with his two dozen spare heads). There are also nine new pieces created for the show, from a giant inflatable "Balloon Boy" in the main atrium to the monster's maw through which one enters the exhibition proper.

The bulk of the work on show consists of drawings, the vast majority offering individual vividness while remaining consistent with Burton's overall sensibility: there are monsters, aliens, fairgrounds and suburbia; creepy-sympathetic figures that are sharp-toothed, spindly-limbed, bristling with stalks and spirals but often bulbously top-heavy or buxomly dominatrixy. Stark black-and-white stripes alternate with splattered palettes of riotous, even fluorescent colour.

This consistency is striking and limiting. There's really not that much difference in sensibility and technique between Burton's latest works and the paintings of alien invasions or monstrous animations created during his adolescence. Impressive stuff for a teenager, no question, but it leaves the show feeling awfully samey. Even the novelty value of glimpses of early or uncompleted projects is qualified by a feeling that if we never saw Burton's Hansel and Gretel or Little Dead Riding Hood, we can probably imagine how they would look without much difficulty. Nor, a couple of installation pieces notwithstanding, does the show give you the feeling of being in Burton's world yourself in the way that, say, the unsettlingly immersive 2007 David Lynch exhibition at Paris's Fondation Cartier, with its disorienting red curtains and grinding industrial soundtrack, did.

All the more reason, then, for the exhibition to look beyond the contents of Burton's metaphorical garage. There are obvious connections to be made here: with other popular illustrators, such as Charles Addams, Edward Gorey, Ralph Steadman, Ronald Searle and Maurice Sendak; with ideas of childhood, sexuality and outsiderdom that could easily encompass the Grimms, Poe and Freud; and with cinematic movements such as German expressionism and classic monster movies. A Moma film season running in conjunction with the show, called The Lurid Beauty of Monsters, juxtaposes Burton's features with just these kinds of cinematic reference points (Nosferatu, The Brain That Wouldn't Die, Tex Avery cartoons, etc). But the response to the main exhibition is a bit like the response you might have to many of Burton's characters: have you thought about getting out a bit more?